If $f(x)=a x^2+b x+c$ satisfies $f(1)+2 f(2)=0$ and $2 \mathrm{f}(1)+\mathrm{f}(2)=0$, then $3 \mathrm{a}+\mathrm{b}=$

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Aicharya · Accepted Answer

$f(x)=a x^2+b x+c$ (Given) $ \Rightarrow \mathrm{f}(1)=\mathrm{a}+\mathrm{b}+\mathrm{c} $ $ 2 \mathrm{f}(2)=2(4 \mathrm{a}+2 \mathrm{~b}+\mathrm{c}) $ since $f(1)+f(2)=0$ $ \Rightarrow 9 \mathrm{a}+5 \mathrm{~b}+3 \mathrm{c}=0...(i) $ similarly $ 6 a+4 b+3 c=0...(ii) $ now subtracting (ii) from (i) we get $3 a+b=0$

If $f(x)=a x^2+b x+c$ satisfies $f(1)+2 f(2)=0$ and $2 \mathrm{f}(1)+\mathrm{f}(2)=0$, then $3…

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